Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius
type: Item
instance of: scholarly article
title: Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius
zbMATH Open document ID: 1009.31003
DOI: 10.1215/S0012-7094-02-11313-1
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: The main theorems of this paper are: a multiple integral inequality for convex domains \(D\subseteq \mathbb{R}^n\) of finite inradius \[ R_D:=\sup\{R>0 : \exists \text{ ball of radius } R \text{ in } D\} \] and a sharper inequality in \(\mathbb R^2\). Thus, results from [\textit{R. Banuelos, R. Latala} and \textit{P. J. Méndez-Hernández}, Proc. Am. Math. Soc. 129, 2997-3008 (2001; Zbl 0974.60037)] are generalized. These inequalities yield various new isoperimetric-type inequalities for: Brownian motion, symmetric stable processes (in convex domains of finite inradius) and also to processes whose generators are relativistic Schrödinger operators.
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1820903
zbMATH Keywords: inradius
zbMATH Keywords: generalized isoperimetric inequalities
zbMATH Keywords: Brownian motion
zbMATH Keywords: symmetric stable processes
author: Pedro J. Méndez-Hernández
reviewed by: Liliana Popa
MaRDI profile type: Publication
cites work: Q3876353
cites work: Brownian motion and the fundamental frequency of a drum
cites work: Inradius and integral means for Green’s functions and conformal mappings
cites work: An isoperimetric-type inequality for integrals of Green's functions
cites work: Isoperimetric-type bounds for solutions of the heat equation
cites work: A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes
cites work: Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps
cites work: Some Theorems on Stable Processes
cites work: A general rearrangement inequality for multiple integrals
cites work: Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions
cites work: Intrinsic ultracontractivity and conditional gauge for symmetric stable processes
cites work: Estimates on Green functions and Poisson kernels for symmetric stable processes
cites work: Sur la frequence fondamentale d'une membrane vibrante: evaluations par defaut et principe de maximum
cites work: Generalized Isoperimetric Inequalities
cites work: Isoperimetric Inequalities in Mathematical Physics. (AM-27)
cites work: A Lower Bound for the Fundamental Frequency of a Convex Region
cites work: Convex Analysis
cites work: Q4937701
cites work: Maximum principles and their applications
cites work: Mean curvature and the heat equation
full work available at URL: s0012-7094-02-11313-1
OpenAlex ID: W1568868378
description: scientific article; zbMATH DE number 1820903